[en] The behaviour of a one-dimensional system perturbed by a low frequency, periodic electric field is examined in the limit as the field frequency, Ω, tends to zero, that is the static field limit. In particular we obtain estimates of the widths of each member of the infinite set of resonances between any finite value of Ω and 0. In order to obtain this estimate we derive a new analytic approximation of the two-state equations of motion. Our analysis shows why recent experiments on the ionization of excited hydrogen atoms by low frequency fields failed to observe any resonances. (author)